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The rapid growth of data in water resources has created new opportunities to accelerate knowledge discovery with the use of advanced deep learning tools. Hybrid models that integrate theory with state-of-the art empirical techniques have the potential to improve predictions while remaining true to physical laws. This paper evaluates the Process-Guided Deep Learning (PGDL) hybrid modeling framework with a use-case of predicting depth-specific lake water temperatures. The PGDL model has three primary components: a deep learning model with temporal awareness (long short-term memory recurrence), theory-based feedback (model penalties for violating conversation of energy), and model pretraining to initialize the network with synthetic data (water temperature predictions from a process-based model). In situ water temperatures were used to train the PGDL model, a deep learning (DL) model, and a process-based (PB) model. Model performance was evaluated in various conditions, including when training data were sparse and when predictions were made outside of the range in the training data set. The PGDL model performance (as measured by root-mean-square error (RMSE)) was superior to DL and PB for two detailed study lakes, but only when pretraining data included greater variability than the training period. The PGDL model also performed well when extended to 68 lakes, with a median RMSE of 1.65 degrees C during the test period (DL: 1.78 degrees C, PB: 2.03 degrees C; in a small number of lakes PB or DL models were more accurate). This case-study demonstrates that integrating scientific knowledge into deep learning tools shows promise for improving predictions of many important environmental variables. ; Department of the Interior Northeast Climate Adaptation Science Center; Midwest Glacial Lakes Fish Habitat Partnership grant through FWS; NSF Expedition in Computing Grant [1029711]; NSFNational Science Foundation (NSF) [EAR-PF-1725386]; Digital Technology Center at the University of MinnesotaUniversity of Minnesota System; Department of the Interior North Central Climate Adaptation Science Center; North Temperate Lakes Long-Term Ecological Research [NSF DEB-1440297]; Global Lake Ecological Observatory Network [NSF 1702991] ; See supporting information for data access, extended methods details, and example code. See https://doi.org/10.5066/P9AQPIVD for this study's data release and https://doi.org/10.5281/zenodo.3497495 for the versioned code repository. This research was funded by the Department of the Interior Northeast and North Central Climate Adaptation Science Centers, a Midwest Glacial Lakes Fish Habitat Partnership grant through F&WS, NSF Expedition in Computing Grant 1029711 to the University of Minnesota, a postdoctoral fellowship awarded to J.A.Z. under NSF EAR-PF-1725386, and a seed grant from the Digital Technology Center at the University of Minnesota. Access to computing facilities was provided by the University of Minnesota Supercomputing Institute and USGS Advanced Research Computing, USGS Yeti Supercomputer (https://doi.org/10.5066/F7D798MJ). We thank North Temperate Lakes Long-Term Ecological Research (NSF DEB-1440297) and Global Lake Ecological Observatory Network (NSF 1702991) for modeling discussions and data sharing, and Arka Daw, Randy Hunt, Jeff Sadler, Emily Read, and Mike Fienen for the PGDL discussions and ideas. We thank Luke Winslow, Noah Lottig, Madeline Magee, and along with MN DNR and WI DNR for temperature and bathymetric data, with special thanks to Pete Jacobson, Katie Hein, and Madeline Humphrey for collating thousands of temperature records, and Dave Wolock, the editorial group at WRR, and three anonymous reviewers for input that was used to improve this paper. ; Public domain authored by a U.S. government employee

The General Lake Model (GLM) is a one-dimensional open-source code designed to simulate the hydrodynamics of lakes, reservoirs, and wetlands. GLM was developed to support the science needs of the Global Lake Ecological Observatory Network (GLEON), a network of researchers using sensors to understand lake functioning and address questions about how lakes around the world respond to climate and land use change. The scale and diversity of lake types, locations, and sizes, and the expanding observational datasets created the need for a robust community model of lake dynamics with sufficient flexibility to accommodate a range of scientific and management questions relevant to the GLEON community. This paper summarizes the scientific basis and numerical implementation of the model algorithms, including details of sub-models that simulate surface heat exchange and ice cover dynamics, vertical mixing, and inflow-outflow dynamics. We demonstrate the suitability of the model for different lake types that vary substantially in their morphology, hydrology, and climatic conditions. GLM supports a dynamic coupling with biogeochemical and ecological modelling libraries for integrated simulations of water quality and ecosystem health, and options for integration with other environmental models are outlined. Finally, we discuss utilities for the analysis of model outputs and uncertainty assessments, model operation within a distributed cloud-computing environment, and as a tool to support the learning of network participants. © 2019 Author(s). ; Acknowledgements. The primary code for GLM has been developed by Matthew R. Hipsey, Louise C. Bruce, Casper Boon, Brendan Busch, and David P. Hamilton at the University of Western Australia in collaboration with researchers participating in GLEON, with support provided by a National Science Foundation (NSF) (USA) Research Coordination Network Award. Whilst GLM is a new code, it is based on the large body of historical research and publications produced by the Centre for Water Research at the University of Western Australia, which we acknowledge for the inspiration, development, and testing of several of the model approaches that have been adopted. Funding for the initial development of the GLM code was from the U.S. NSF Cyber-enabled Discovery and Innovation grant awarded to Paul C. Hanson (lead investigator) and colleagues from 20092014 (NSF CDI-0941510); subsequent development was supported by the Australian Research Council projects awarded to Matthew R. Hipsey and colleagues (ARC projects LP0990428, LP130100756, and DP130104078). Funding for the optimization and improvement of the snow and ice model was provided by NSF MSB-1638704. Funding for the development of the GLM teaching module and GRAPLEr was provided by NSF ACI-1234983 and NSF EF-1702506 awarded to Cayelan C. Carey. Funding for glmtools was provided by the Department of the Interior Northeast Climate Science Center. Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the U.S. Government. Provision of the environmental symbols used for the GLM scientific diagrams are courtesy of the Integration and Application Network, University of Maryland Center for Environmental Science. Joanne Moo and Aditya Singh also provided support in model set-up and testing. We gratefully acknowledge the anonymous reviewers whose contribution and editing have significantly improved the paper and model.

The modelling community has identified challenges for the integration and assessment of lake models due to the diversity of modelling approaches and lakes. In this study, we develop and assess a one-dimensional lake model and apply it to 32 lakes from a global observatory network. The data set included lakes over broad ranges in latitude, climatic zones, size, residence time, mixing regime and trophic level. Model performance was evaluated using several error assessment metrics, and a sensitivity analysis was conducted for nine parameters that governed the surface heat exchange and mixing efficiency. There was low correlation between input data uncertainty and model performance and predictions of temperature were less sensitive to model parameters than prediction of thermocline depth and Schmidt stability. The study provides guidance to where the general model approach and associated assumptions work, and cases where adjustments to model parameterisations and/or structure are required. (c) 2017 Published by Elsevier Ltd. ; Australian Research Council (ARC)Australian Research Council [DP130104078, LP130100756] ; GLM development and funding support for LCB, BDB, CB and MRH was provided by the Australian Research Council (ARC) (grants DP130104078 & LP130100756). Additional contributions from individuals and organisations as well as sources of data, provided from a variety of organisations are summarised in Appendix D. This study was made possible through the sharing of ideas, data and models across the AEMON and GLEON networks as well as discussions and working groups held during AEMON workshops and GLEON meetings. ; Public domain authored by a U.S. government employee